If a person walks with a speed of 1.1 miles per hour, it takes 195 minutes to walk around the rim. Assuming that the rim is approximately a circle, what is the diameter of the crater? (Round your answer to the nearest tenth and make sure you convert the minutes to hours first!) b . How many cubic miles of sand would fill the crater if its approximate shape is a hemisphere (half of a sphere)? The volume of the whole sphere is V = 4 3 π r 3 . Round your answer to the nearest hundredth. cubic miles

Accepted Solution

Answer:a) 1.138 milesb) 0.385 miles³Step-by-step explanation:Data provided:Speed = 1.1 miles per hourTime taken to travel around the rim = 195 minutesNow,1 hour = 60 minutesthus, 195 minutes = [tex]\frac{\textup{195}}{\textup{60}}[/tex]  = 3.25 hoursHence, The total distance covered around the rim = speed × time or= 1.1 × 3.25 = 3.575 milesa) Distance around the rim of crater = πdwhere, d is the diameter of the craterorπd = 3.575ord = 1.138 milesor radius of the crater, r = [tex]\frac{\textup{d}}{\textup{2}}[/tex] =[tex]\frac{\textup{1.138}}{\textup{2}}[/tex]  = 0.569 milesb) NowVolume of hemisphere = [tex]\frac{\textup{1}}{\textup{2}}\times(\textup{volume of whole sphere})[/tex] volume of whole sphere = [tex]\frac{\textup{4}}{\textup{3}}\pi r^3[/tex] orvolume of whole sphere = [tex]\frac{\textup{4}}{\textup{3}}\pi\times0.569^3[/tex] orvolume of whole sphere = 0.771 miles³Therefore, The Volume of hemisphere = [tex]\frac{\textup{1}}{\textup{2}}\times(\textup{0.771})[/tex] orThe Volume of hemisphere = 0.385 miles³